it would definitely help to know what type of game it was. was it an internet flash game? did it come on a cd from a store? etcetera.
then you could use google to help you find a list of games.
for instance lets say its a puzzle game for windows... you could search for "puzzle game list for windows" and maybe you will get lucky.
my guess is that such a simple game would have a name like "animal hunter", "fur trapper", or some other name which will jump right out at you from a list.
its going to take awhile to find it though
the other option is to find a forum devoted to gaming. preferably puzzles. you can then ask around there as people with the same interests as you (puzzle games) might have a better idea.